Factor Calculator

Factors of 585

The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585. In total, 585 has 12 factors. Its prime factorization is 3² × 5 × 13, and the sum of all its factors is 1092.

All factors of 585

Here are all 12 factors of 585, listed from smallest to largest.

13591315394565117195585

Factor pairs of 585

These 6 pairs of whole numbers each multiply to give 585.

1 × 585 = 585
3 × 195 = 585
5 × 117 = 585
9 × 65 = 585
13 × 45 = 585
15 × 39 = 585

Prime factorization of 585

Dividing 585 by the smallest prime at each step gives its prime factorization:

585 ÷ 3 = 195
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
Result: 585 = 3 × 3 × 5 × 13 = 3² × 5 × 13

The distinct prime factors of 585 are 3, 5, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 585

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 5855853195365513
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 585

Number of factors12
Sum of factors1092
Sum of proper factors507
Prime factorization3² × 5 × 13
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 585 interesting

  • 585 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 585 is a deficient number: its proper factors sum to 507, which is 78 less than 585 itself.
  • 585 has 3 distinct prime factors (3, 5, 13), which is why it has so many divisors.

How to find the factors of 585 yourself

Divide 585 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √585 ≈ 24.19, because every factor above that pairs with one below it.

585 ÷ 1 = 585 ✓
585 ÷ 3 = 195 ✓
585 ÷ 5 = 117 ✓
585 ÷ 9 = 65 ✓
585 ÷ 13 = 45 ✓
585 ÷ 15 = 39 ✓

Reading both columns gives every factor: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585. The factor calculator does this automatically for any number.

Numbers mathematically connected to 585.

Frequently asked questions about 585

What are the factors of 585?

The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585. That is 12 factors in total, counting both 1 and 585.

Is 585 a prime number?

No, 585 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 585 is also divisible by 3.

What is the prime factorization of 585?

The prime factorization of 585 is 3² × 5 × 13. Written out in full: 3 × 3 × 5 × 13 = 585. Its distinct prime factors are 3, 5, 13.

What two numbers multiply to give 585?

There are 6 pairs of whole numbers that multiply to 585: 1 × 585, 3 × 195, 5 × 117, 9 × 65, 13 × 45, 15 × 39.

What is the sum of the factors of 585?

Adding all the factors of 585 together gives 1092. Excluding 585 itself, the proper factors sum to 507.

Is 585 a perfect square?

No, 585 is not a perfect square. There is no whole number that multiplies by itself to give 585. The nearest perfect squares are 576 and 625.

What is the largest factor of 585 other than itself?

The largest factor of 585 apart from 585 itself is 195, since 585 ÷ 195 = 3.

How many factors does 585 have?

585 has 12 factors: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585. You can verify this from the prime factorization 3² × 5 × 13: add 1 to each exponent and multiply, giving 3 × 2 × 2 = 12.

Explore more

Try another number in the factor calculator, break 585 down further with the prime factorization calculator, or compare 585 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.